Find the diameter $ d $ of a cone if height $h = 11$ and volume $V = 564$.

$d = 46.4147$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ V = \dfrac{ r ^{ 2 } \cdot h \cdot \pi}{ 3 } $$

After substituting $ V = 564 $ and $ h = 11 $ we have:

$$ 564 = \dfrac{ r ^{ 2 } \cdot 11 \cdot \pi}{ 3 } $$$$ 564 \cdot 3 = r ^{ 2 } \cdot 11 \cdot \pi $$$$ 1692 = 11 \cdot r ^{ 2 } \cdot \pi $$$$ r ^{ 2 } = \dfrac{ 1692}{ 11 \, \pi } $$$$ r ^{ 2 } = 538.5808 $$$$ r = \sqrt{ 538.5808 } $$$$ r = 23.2073 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $ r = 23.2073 $ we have:

$$ d = 2 \cdot 23.2073 $$ $$ d \approx 46.4147 $$

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